Hello

Obtain the solution of the following differential equation as a power series about the origin :

Solution:

Let

then :

Rewrite the equation as :

and substitute the values of y & y'' gives:

or:

My problem is in the last summation

I want to make the summations start with the same n and the powers of the x's are n in order to get the recursive relation, but I can not do that .

the last summation makes my life hard

any help?